Subgroups — C₃×C₅×#3176 #14276210

Order 1920.

772 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#540	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×#499	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#493	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#490	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#469	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#466	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#442	C₂	1	2	yes	maximal, complemented
8	C₃×C₄×C₅×D₈	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#405	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#3176	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃×C₅×D₈	C₂²	1	2	yes	—
12	C₂×C₃×C₅×D₈	C₂²	1	2	yes	—
13	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
15	C₃×C₅×#127	C₂²	1	2	yes	—
16	C₃×C₅×#125	C₂²	1	2	yes	—
17	C₃×C₅×#123	—	2	4	no	—
18	C₃×C₅×#121	—	2	4	no	—
19	C₃×C₅×#121	C₂²	1	4	yes	—
20	C₃×C₄×C₅×D₄	C₂²	1	4	yes	—
21	C₃×C₅×#117	C₂²	1	1	yes	characteristic
22	C₃×C₅×#107	C₂²	1	2	yes	—
23	C₃×C₅×#106	C₂²	1	2	yes	—
24	C₃×C₅×#102	C₂²	1	4	yes	—
25	C₃×C₅×#102	C₂²	1	4	yes	—
26	C₃×C₅×#97	C₂²	1	1	yes	characteristic
27	C₃×C₅×#97	C₂²	1	1	yes	characteristic
28	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
29	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
30	C₃×#3176	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
31	C₅×#540	C₂×C₃	1	2	yes	complemented
32	C₅×#499	C₂×C₃	1	1	yes	characteristic, complemented
33	C₅×#493	C₂×C₃	1	1	yes	characteristic, complemented
34	C₅×#490	C₂×C₃	1	2	yes	complemented
35	C₅×#469	C₂×C₃	1	2	yes	complemented
36	C₅×#466	C₂×C₃	1	2	yes	complemented
37	C₅×#442	C₂×C₃	1	2	yes	complemented
38	C₄×C₅×D₈	C₂×C₃	1	2	yes	complemented
39	C₅×#405	C₂×C₃	1	1	yes	characteristic, complemented
40	C₂×C₃×C₅×D₄	—	2	4	no	—
41	C₂×C₃×C₅×D₄	—	2	4	no	—
42	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
43	C₂²×C₃×C₄×C₅	—	2	4	no	—
44	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
45	C₃×C₅×D₈	—	2	4	no	—
46	C₃×C₅×D₈	—	2	4	no	—
47	C₃×C₅×M₁₆	—	2	2	no	—
48	C₂×C₃×C₅×C₈	—	2	2	no	—
49	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
50	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
51	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
52	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
53	C₃×C₅×C₄⋊C₄	—	2	4	no	—
54	C₃×C₅×C₄⋊C₄	D₄	1	2	yes	—
55	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
56	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
57	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
58	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
59	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
60	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
61	C₃×#540	C₂×C₅	1	2	yes	complemented
62	C₃×#499	C₂×C₅	1	1	yes	characteristic, complemented
63	C₃×#493	C₂×C₅	1	1	yes	characteristic, complemented
64	C₃×#490	C₂×C₅	1	2	yes	complemented
65	C₃×#469	C₂×C₅	1	2	yes	complemented
66	C₃×#466	C₂×C₅	1	2	yes	complemented
67	C₃×#442	C₂×C₅	1	2	yes	complemented
68	C₃×C₄×D₈	C₂×C₅	1	2	yes	complemented
69	C₃×#405	C₂×C₅	1	1	yes	characteristic, complemented
70	C₂×C₅×D₈	C₂²×C₃	1	2	yes	—
71	C₂×C₅×D₈	C₂²×C₃	1	2	yes	—
72	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
73	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
74	C₅×#127	C₂²×C₃	1	2	yes	—
75	C₅×#125	C₂²×C₃	1	2	yes	—
76	C₅×#123	—	2	4	no	—
77	C₅×#121	—	2	4	no	—
78	C₅×#121	C₂²×C₃	1	4	yes	—
79	C₄×C₅×D₄	C₂²×C₃	1	4	yes	—
80	C₅×#117	C₂²×C₃	1	1	yes	characteristic
81	C₅×#107	C₂²×C₃	1	2	yes	—
82	C₅×#106	C₂²×C₃	1	2	yes	—
83	C₅×#102	C₂²×C₃	1	4	yes	—
84	C₅×#102	C₂²×C₃	1	4	yes	—
85	C₅×#97	C₂²×C₃	1	1	yes	characteristic
86	C₅×#97	C₂²×C₃	1	1	yes	characteristic
87	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
88	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
89	#3176	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
90	C₂³×C₃×C₅	—	2	4	no	—
91	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
92	C₃×C₅×D₄	—	2	4	no	—
93	C₃×C₅×D₄	—	2	4	no	—
94	C₃×C₅×D₄	—	8	4	no	—
95	C₃×C₅×D₄	—	8	4	no	—
96	C₂×C₃×C₄×C₅	—	2	1	no	—
97	C₂×C₃×C₄×C₅	—	2	1	no	—
98	C₂×C₃×C₄×C₅	—	2	4	no	—
99	C₂×C₃×C₄×C₅	—	8	4	no	—
100	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
101	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
102	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
103	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
104	C₃×C₅×C₈	—	2	1	no	—
105	C₃×C₅×C₈	—	2	1	no	—
106	C₃×C₅×C₈	#41	1	2	yes	—
107	C₃×C₅×C₈	#41	1	2	yes	—
108	C₂×C₃×D₈	C₂²×C₅	1	2	yes	—
109	C₂×C₃×D₈	C₂²×C₅	1	2	yes	—
110	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
111	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
112	C₃×#127	C₂²×C₅	1	2	yes	—
113	C₃×#125	C₂²×C₅	1	2	yes	—
114	C₃×#123	—	2	4	no	—
115	C₃×#121	—	2	4	no	—
116	C₃×#121	C₂²×C₅	1	4	yes	—
117	C₃×C₄×D₄	C₂²×C₅	1	4	yes	—
118	C₃×#117	C₂²×C₅	1	1	yes	characteristic
119	C₃×#107	C₂²×C₅	1	2	yes	—
120	C₃×#106	C₂²×C₅	1	2	yes	—
121	C₃×#102	C₂²×C₅	1	4	yes	—
122	C₃×#102	C₂²×C₅	1	4	yes	—
123	C₃×#97	C₂²×C₅	1	1	yes	characteristic
124	C₃×#97	C₂²×C₅	1	1	yes	characteristic
125	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
126	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
127	C₂×C₅×D₄	—	2	4	no	—
128	C₂×C₅×D₄	—	2	4	no	—
129	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
130	C₂²×C₄×C₅	—	2	4	no	—
131	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
132	C₅×D₈	—	2	4	no	—
133	C₅×D₈	—	2	4	no	—
134	C₅×M₁₆	—	2	2	no	—
135	C₂×C₅×C₈	—	2	2	no	—
136	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
137	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
138	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
139	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
140	C₅×C₄⋊C₄	—	2	4	no	—
141	C₅×C₄⋊C₄	C₃×D₄	1	2	yes	—
142	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
143	C₅×C₂²⋊C₄	—	2	4	no	—
144	C₅×C₂²⋊C₄	—	2	4	no	—
145	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
146	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
147	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
148	#540	C₂×C₃×C₅	1	2	yes	complemented
149	#499	C₂×C₃×C₅	1	1	yes	characteristic, complemented
150	#493	C₂×C₃×C₅	1	1	yes	characteristic, complemented
151	#490	C₂×C₃×C₅	1	2	yes	complemented
152	#469	C₂×C₃×C₅	1	2	yes	complemented
153	#466	C₂×C₃×C₅	1	2	yes	complemented
154	#442	C₂×C₃×C₅	1	2	yes	complemented
155	C₄×D₈	C₂×C₃×C₅	1	2	yes	complemented
156	#405	C₂×C₃×C₅	1	1	yes	characteristic, complemented
157	C₂²×C₃×C₅	—	2	1	no	—
158	C₂²×C₃×C₅	—	2	2	no	—
159	C₂²×C₃×C₅	—	4	4	no	—
160	C₂²×C₃×C₅	—	4	4	no	—
161	C₂²×C₃×C₅	—	4	4	no	—
162	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
163	C₃×C₄×C₅	—	2	1	no	—
164	C₃×C₄×C₅	—	2	2	no	—
165	C₃×C₄×C₅	—	2	2	no	—
166	C₃×C₄×C₅	—	4	4	no	—
167	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
168	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
169	C₂×C₃×D₄	—	2	4	no	—
170	C₂×C₃×D₄	—	2	4	no	—
171	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
172	C₂²×C₃×C₄	—	2	4	no	—
173	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
174	C₃×D₈	—	2	4	no	—
175	C₃×D₈	—	2	4	no	—
176	C₃×M₁₆	—	2	2	no	—
177	C₂×C₃×C₈	—	2	2	no	—
178	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
179	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
180	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
181	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
182	C₃×C₄⋊C₄	—	2	4	no	—
183	C₃×C₄⋊C₄	C₅×D₄	1	2	yes	—
184	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
185	C₃×C₂²⋊C₄	—	2	4	no	—
186	C₃×C₂²⋊C₄	—	2	4	no	—
187	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
188	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
189	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
190	C₂³×C₅	—	2	4	no	—
191	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
192	C₅×D₄	—	2	4	no	—
193	C₅×D₄	—	2	4	no	—
194	C₅×D₄	—	8	4	no	—
195	C₅×D₄	—	8	4	no	—
196	C₂×C₄×C₅	—	2	1	no	—
197	C₂×C₄×C₅	—	2	1	no	—
198	C₂×C₄×C₅	—	2	4	no	—
199	C₂×C₄×C₅	—	8	4	no	—
200	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
201	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
202	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
203	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
204	C₅×C₈	—	2	1	no	—
205	C₅×C₈	—	2	1	no	—
206	C₅×C₈	C₃×#41	1	2	yes	—
207	C₅×C₈	C₃×#41	1	2	yes	—
208	C₂×D₈	C₂²×C₃×C₅	1	2	yes	—
209	C₂×D₈	C₂²×C₃×C₅	1	2	yes	—
210	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
211	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
212	#127	C₂²×C₃×C₅	1	2	yes	—
213	#125	C₂²×C₃×C₅	1	2	yes	—
214	#123	—	2	4	no	—
215	#121	—	2	4	no	—
216	#121	C₂²×C₃×C₅	1	4	yes	—
217	C₄×D₄	C₂²×C₃×C₅	1	4	yes	—
218	#117	C₂²×C₃×C₅	1	1	yes	characteristic
219	#107	C₂²×C₃×C₅	1	2	yes	—
220	#106	C₂²×C₃×C₅	1	2	yes	—
221	#102	C₂²×C₃×C₅	1	4	yes	—
222	#102	C₂²×C₃×C₅	1	4	yes	—
223	#97	C₂²×C₃×C₅	1	1	yes	characteristic
224	#97	C₂²×C₃×C₅	1	1	yes	characteristic
225	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
226	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
227	C₂×C₃×C₅	—	4	1	no	—
228	C₂×C₃×C₅	—	8	4	no	—
229	C₂×C₃×C₅	#532	1	1	yes	characteristic
230	C₂×C₃×C₅	#576	1	2	yes	—
231	C₂³×C₃	—	2	4	no	—
232	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
233	C₃×D₄	—	2	4	no	—
234	C₃×D₄	—	2	4	no	—
235	C₃×D₄	—	8	4	no	—
236	C₃×D₄	—	8	4	no	—
237	C₂×C₃×C₄	—	2	1	no	—
238	C₂×C₃×C₄	—	2	1	no	—
239	C₂×C₃×C₄	—	2	4	no	—
240	C₂×C₃×C₄	—	8	4	no	—
241	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
242	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
243	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
244	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
245	C₃×C₈	—	2	1	no	—
246	C₃×C₈	—	2	1	no	—
247	C₃×C₈	C₅×#41	1	2	yes	—
248	C₃×C₈	C₅×#41	1	2	yes	—
249	C₂²×C₅	—	2	2	no	—
250	C₂²×C₅	—	2	1	no	—
251	C₂²×C₅	—	4	4	no	—
252	C₂²×C₅	—	4	4	no	—
253	C₂²×C₅	—	4	4	no	—
254	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
255	C₄×C₅	—	2	2	no	—
256	C₄×C₅	—	2	2	no	—
257	C₄×C₅	—	2	1	no	—
258	C₄×C₅	—	4	4	no	—
259	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
260	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
261	C₂×D₄	—	2	4	no	—
262	C₂×D₄	—	2	4	no	—
263	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
264	C₂²×C₄	—	2	4	no	—
265	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
266	D₈	—	2	4	no	—
267	D₈	—	2	4	no	—
268	M₁₆	—	2	2	no	—
269	C₂×C₈	—	2	2	no	—
270	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
271	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
272	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
273	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
274	C₄⋊C₄	—	2	4	no	—
275	C₄⋊C₄	C₃×C₅×D₄	1	2	yes	—
276	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
277	C₂²⋊C₄	—	2	4	no	—
278	C₂²⋊C₄	—	2	4	no	—
279	C₂²⋊C₄	C₃×C₅×D₄	1	2	yes	—
280	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
281	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
282	C₃×C₅	#3176	1	1	yes	characteristic, direct product factor, Hall
283	C₂²×C₃	—	2	1	no	—
284	C₂²×C₃	—	2	2	no	—
285	C₂²×C₃	—	4	4	no	—
286	C₂²×C₃	—	4	4	no	—
287	C₂²×C₃	—	4	4	no	—
288	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
289	C₃×C₄	—	2	1	no	—
290	C₃×C₄	—	2	2	no	—
291	C₃×C₄	—	2	2	no	—
292	C₃×C₄	—	4	4	no	—
293	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
294	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
295	C₂×C₅	—	4	1	no	—
296	C₂×C₅	—	8	4	no	—
297	C₂×C₅	C₃×#532	1	1	yes	characteristic
298	C₂×C₅	C₃×#576	1	2	yes	—
299	C₂³	—	2	4	no	—
300	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
301	D₄	—	2	4	no	—
302	D₄	—	2	4	no	—
303	D₄	—	8	4	no	—
304	D₄	—	8	4	no	—
305	C₂×C₄	—	2	1	no	—
306	C₂×C₄	—	2	1	no	—
307	C₂×C₄	—	2	4	no	—
308	C₂×C₄	—	8	4	no	—
309	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
310	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
311	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
312	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
313	C₈	—	2	1	no	—
314	C₈	—	2	1	no	—
315	C₈	C₃×C₅×#41	1	2	yes	—
316	C₈	C₃×C₅×#41	1	2	yes	—
317	C₂×C₃	—	4	1	no	—
318	C₂×C₃	—	8	4	no	—
319	C₂×C₃	C₅×#532	1	1	yes	characteristic
320	C₂×C₃	C₅×#576	1	2	yes	—
321	C₅	C₃×#3176	1	1	yes	characteristic, direct product factor, Sylow
322	C₂²	—	2	1	no	—
323	C₂²	—	2	2	no	—
324	C₂²	—	4	4	no	—
325	C₂²	—	4	4	no	—
326	C₂²	—	4	4	no	—
327	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
328	C₄	—	2	1	no	—
329	C₄	—	2	2	no	—
330	C₄	—	2	2	no	—
331	C₄	—	4	4	no	—
332	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
333	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
334	C₃	C₅×#3176	1	1	yes	characteristic, direct product factor, Sylow
335	C₂	—	4	1	no	—
336	C₂	—	8	4	no	—
337	C₂	C₃×C₅×#532	1	1	yes	characteristic
338	C₂	C₃×C₅×#576	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₃×C₅×#117 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃×C₅×#540	C₂	semidirect
2. C₃×C₅×#499	C₂	semidirect
3. C₃×C₅×#493	C₂	semidirect
4. C₃×C₅×#490	C₂	semidirect
5. C₃×C₅×#469	C₂	semidirect
6. C₃×C₅×#466	C₂	semidirect
7. C₃×C₅×#442	C₂	semidirect
8. C₃×C₄×C₅×D₈	C₂	semidirect
9. C₃×C₅×#405	C₂	semidirect
10. C₅×#3176	C₃	direct (N × H)
30. C₃×#3176	C₅	direct (N × H)
31. C₅×#540	C₂×C₃	semidirect
32. C₅×#499	C₂×C₃	semidirect
33. C₅×#493	C₂×C₃	semidirect
34. C₅×#490	C₂×C₃	semidirect
35. C₅×#469	C₂×C₃	semidirect
36. C₅×#466	C₂×C₃	semidirect
37. C₅×#442	C₂×C₃	semidirect
38. C₄×C₅×D₈	C₂×C₃	semidirect
39. C₅×#405	C₂×C₃	semidirect
61. C₃×#540	C₂×C₅	semidirect
62. C₃×#499	C₂×C₅	semidirect
63. C₃×#493	C₂×C₅	semidirect
64. C₃×#490	C₂×C₅	semidirect
65. C₃×#469	C₂×C₅	semidirect
66. C₃×#466	C₂×C₅	semidirect
67. C₃×#442	C₂×C₅	semidirect
68. C₃×C₄×D₈	C₂×C₅	semidirect
69. C₃×#405	C₂×C₅	semidirect
89. #3176	C₃×C₅	direct (N × H)
148. #540	C₂×C₃×C₅	semidirect
149. #499	C₂×C₃×C₅	semidirect
150. #493	C₂×C₃×C₅	semidirect
151. #490	C₂×C₃×C₅	semidirect
152. #469	C₂×C₃×C₅	semidirect
153. #466	C₂×C₃×C₅	semidirect
154. #442	C₂×C₃×C₅	semidirect
155. C₄×D₈	C₂×C₃×C₅	semidirect
156. #405	C₂×C₃×C₅	semidirect
282. C₃×C₅	#3176	direct (N × H)
321. C₅	C₃×#3176	direct (N × H)
334. C₃	C₅×#3176	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₅×#540	2
C₃×C₅×#499	2
C₃×C₅×#493	2
C₃×C₅×#490	2
C₃×C₅×#469	2
C₃×C₅×#466	2
C₃×C₅×#442	2
C₃×C₄×C₅×D₈	2
C₃×C₅×#405	2
C₅×#3176	3
C₃×#3176	5

Subgroups — C3×C5×#3176 #14276210

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3176 #14276210